AFCRL-TR-73-0107

RESISTIVITY AND CARRIER LIFETIME

IN GOLD-DOPED SILICON

by

W. Robert Thurber, David C. Lewis, and W. Murray Bull is

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

PRO Y-72-873

Project No. 6095

Task No. 609604

Work Unit No. 60960401

FINAL REPORT

Period Covered: 1 January 1972 - 31 December 1972

January 31, 1973

Contract Monitor: D. Eirug Davies, Solid State Sciences Laboratory

Approved for public release; distribution unlimited.

Prepared

for

AIR FORCE CAMBRIDGE RESEARCH LABORATORIES

AIR FORCE SYSTEMS COMMAND

UNITED STATES AIR FORCE

BEDFORD. MASSACHUSEHS 01730

AFCRL-TR-73-0107

RESISTIVITY AND CARRIER LIFETIME

I N GOLD-DOPED SILICON

by

W. Robert Thurber, David C. Lewis, and W. Murray Bull is

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

PRO Y-72-873

Project No. 6096

Task No. 609604

Work Unit No. 60960401

FINAL REPORT

Period Covered: 1 January 1972 - 31 December 1972

January 31, 1973

Contract Monitor: D. Eirug Davies, Solid State Sciences Laboratory

Approved for public release; distribution unlimited.

Prepared

for

AIR FORCE CAMBRIDGE RESEARCH LABORATORIES

AIR FORCE SYSTEMS COMMAND

UNITED STATES AIR FORCE

BEDFORD. MASSACHUSETTS 01730
Qualified requestors may obtain additional copies from

the Defense Documentation Center. All others should

apply to the National Technical Information Service.
ABSTRACT

This report describes the current status of a continuing

study of the electrical properties of gold-doped silicon. Room

temperature resistivity and Hall effect measurements were made

on many sets of gold-diffused, boron- or phosphorus-doped silicon

wafers for a wide range of initial resistivities of both types.

The general suitability of the proposed model was verified although

an apparent discrepancy still remains between total and electrically

active gold as confirmed by resistivity data as a function of gold

density for phosphorus-doped silicon. Electrical measurements were

made to study the activation energies of the gold donor and acceptor.

In addition the activation energy of the gold-coupled shallow acceptor in the proposed model was observed. The values found were in

good agreement with other reported observations of these levels.

In the application of the surface photovoltage method to the mea- surement of minority carrier lifetime, it was found that the optical absorption coefficients needed in the analysis of the data were

dependent on the heat treatment given to the specimen. The uncertainty in diffusion length was determined to be about 2 ym which

placed an effective lower limit on lifetime measurements of about

15 ns in p-type and about 50 ns in n-type silicon. An analysis

of the use of the surface photovoltage method for lifetime measurements in thin epitaxial layers is included as an appendix. The reverse recovery (RR) technique for measuring lifetime was examined

and it was observed that the dependence of diode storage time on the ratio of forward to reverse current varied with the base width

of the diode studied. While theory and experiment for open circuit

voltage decay (OCVD) were in agreement for long base width diodes,

correlation for short base diodes was less satisfactory; this study

is continuing. Both the RR and OCVD techniques give the same value

of lifetime for long base diodes, but agreement for short base

diodes is not as good. Additional entries are included as a supplement to an earlier bibliography on the properties of gold-doped

silicon.

iii

CONTENTS

PAGE

Foreword vi

Introduction 1

Specimen Preparation and Determination of Gold Density ... 3

Resistivity and Hall Effect Measurements 5

Resistivity vs. Gold Density in p~Type Silicon .... 5

Resistivity vs> Gold Density in n-Type Silicon .... 8

Activation Energies 14

Carrier Mobility 23

Beat Treatment Studies 23

Carrier Lifetime Measurements 27

Surface Thotovoltage Method 27

Diode Recovery Methods 28

Reverse Recovery Method 29

Open Circuit Voltage Decay Method 32

Comparisons Between RR and OCVD Measurements 34

Directions for Future Work 35

References 37

Appendix A — Specimen Preparation 39

Appendix B — Activation Analysis 41

Appendix C — Interpretation of Steady-State Surface

Photovoltage Measurements in Epitaxial

Semiconductor Layers 43

Appendix D — Supplementary Bibliography: Gold-Doped

Silicon 49

V
FOREWORD

The work reported here is a part of the Joint Program on Methods of

Measurement for Semiconductor Materials, Process Control, and Devices. This

program is carried out at the National Bureau of Standards and receives support from a number of other agencies of the Federal Government in addition

to the NBS. The program was undertaken in 1968 to focus NBS efforts to en- hance the performance, interchangeability , and reliability of discrete semiconductor devices and integrated circuits through improvements in methods of

measurement for use in specifying materials and devices and in control of

device fabrication processes. These improvements are intended to lead to a set of measurement methods which have been carefully evaluated for technical

adequacy, which are acceptable to both users and suppliers, which can provide

a common basis for the purchase specifications of government agencies, and

which will lead to greater economy in government procurement. In addition,

such methods will provide a basis for controlled improvements in essential

device characteristics, such as uniformity of response to radiation effects.

During 1972 the portion of the program concerned with gold-doped silicon re- ceived partial support from the Air Force Cambridge Research Laboratories

(LQD) under project order Y-72-873. The contract monitor was D. E. Davies.

The present project is a follow-on to AFCRL PRO Y-71-906.

Technical personnel who contributed to this effort during the period

covered were:

W. M. Bullis, supervisory physicist, principal investigator

M. Cosman, mechanical engineering technician, specimen

preparation

T. E. Gills, research chemist, neutron activation analysis

J, Krawczyk, physical science technician, diffusion

T. F. Leedy, physicist, diffusion

D. C. Lewis, general physical scientist, diode recovery

measurements and analysis

W. E. Phillips, physicist, surface-photovoltage measurements

P. M. Sandow, general physical scientist, spreading resistance

measurements

A. W. Stallings, mechanical engineering technician, electrical

measurements

W. R. Thurber, physicist, electrical measurements

Preliminary reports of the work have been reported in Joint Program

quarterly progress reports that have been issued in the NBS Technical Note

series. NBS Technical Notes 733, 743, and 754 cover periods during which

support was received under the above noted project order. Earlier work is

reported in NBS Technical Notes 488, 495, 520, 527, 560, 571, 592, 598, 702,

717, and 727.

vi
RESISTIVITY AND CARRIER LIFETIME

IN GOLD-DOPED SILICON

W. Robert Thurber, David C. Lewis, and W. Murray Bullis

INTRODUCTION

Gold is an amphoteric recombination center in silicon. Its addition to

either n-type or p-type silicon will affect the carrier lifetime. No other

impurity addition has been found that is as effective for controlling carrier lifetime in silicon; hence, gold is widely used in device fabrication.

The basic electrical model for the impurity states associated with gold

was clearly enunciated in early work on gold-doped silicon [1], and the diffusion technology for introducing gold into the silicon lattice, though

largely empirical, is under sufficient control that device manufacturers can successfully employ it on a large-scale. Nevertheless, unresolved problems

remain in both areas. In particular, clarification of the details of the

electrical model is necessary before concentrations of gold centers can be

determined unambiguously from measurements of resistivity or carrier lifetime

as might be desired, for example, in bef ore-and-after studies of radiation

effects in gold-doped silicon.

In the work reported here, reasons are being sought for the apparent

discrepancy between total and electrically active gold, for the discrepancy

between calculated and observed resistivity in both n-type and p-type specimens with very large gold concentration, and for the diversity in the capture

cross section data reported in the literature. To investigate these problems, a series of silicon wafers to which various amounts of gold and phosphorus or boron have been added is being characterized by measuring resistivity, Hall coefficient, and carrier lifetime at room temperature. Gold

concentrations are determined directly by neutron activation analysis after

gold has been diffused into the wafer; shallow dopant (phosphorus or boron)

concentrations are determined by measurement of wafer resistivity before gold

diffusion. In addition, ancillary experiments and computations to develop

the diffusion technology necessary to prepare the specimens and to elucidate

certain aspects of proposed models are being carried out.

In earlier phases of this work [2] , specimen preparation, electrical

measurement, and activation analysis procedures were established. From electrical measurements on a limited range of specimens, a model was identified

that appeared to account for the observed resistivity of p-type silicon

heavily doped with gold. In addition the surface photovoltage technique for

measuring minority carrier diffusion length was studied extensively. Two

difficulties were encountered in applying this technique to gold-doped silicon specimens. First, the uncertainty in diffusion length was found to be

about 1 or 2 ym which placed an effective lower limit on lifetime measurements of about 15 ns in p-type silicon and about 50 ns in n-type silicon.

Second, the optical absorption coefficient data needed in the analysis of

the measurements was dependent on the heat treatment given to the specimen.

1
During the period covered by the present report the electrical studies

were almost completed and the general suitability of the proposed model was

confirmed. Additional analysis of the data was undertaken to seek an explanation for the apparent discrepancy between total and electrically active

gold, but no satisfactory result was obtained. Electrical measurements were

also studied to obtain the energy levels of the gold donor and acceptor. In

addition, the energy level of the gold-coupled shallow acceptor in the proposed model was also observed, confirming the result reported by Bruckner [3].

Additional studies of the steady-state surface photovoltage (SPV) method

were conducted with particular emphasis on the problems of accurate absorption coefficient data and of experimental reproducibility for short diffusion

length measurements. A detailed analysis of the application of the SPV method to measurements in thin epitaxial layers was completed and published. Be- cause of the limitations of this method for measurement of short lifetimes,

attention was redirected toward reverse recovery and open circuit voltage

decay measurements. Considerable insight into the previously observed discrepancies between these methods has been developed in this study which is

still underway.

2
SPECIMEN PREPARATION AND DETERMINATION OF GOLD DENSITY

Both n-type and p-type crystals doped with phosphorus and boron, respectively are being studied. About ten resistivity values of each type cover the

range 0.01 to 2500 Q'cm as listed in table 1. Specimens were prepared for

electrical measurements and gold density determinations in essentially the same manner as used during the previous work [2], Details are given in Appendix A.

Gold densities were determined by neutron activation analysis by the

second of the two procedures described previously [2], Details are given in

Appendix B.

3
Table 1 — Silicon Crystals for Gold Diffusion

Initial Resistivity Type Pulled or Status

p . , fi • cm Float Zoned

'\^0.01 n f-2 available

•^0.01 V f-z available

'^0.08 n pulled available

0.076 P pulled measured

0,30 n f-z measured

0.53 V pulled measured

1.0 n f-z measured

1.1 P pulled measured

5.3 n pulled measured

11 P pulled measured

'^20 n f-z available

20 P f-z measured

75 n f-z. measured

93 P

f-z measured

380 n f-2 measured

280 P f-z measured

"^1000 n f-z available

1100 P f-z measured

2300 f-z measured

2300 P f-z measured

2700 P pulled measured

4
RESISTIVITY AND HALL EFFECT MEASUREMENTS

Resistivity vs. Gold Density in p-Type Silicon — During this period,

resistivity measurements were made on boron-doped silicon wafers with initial

room-temperature resistivities (before the addition of gold) of 0.076, 0.53,

1.1, 280, 1100, 2300, and 2700 fi«cm. The gold density ranged from about

lO^'* cm~^ to about 10^^ cm~^. The resistivity of these, and previously measured initially 11-, 20-, and 93-fl*cm specimens, is shown as a function of

gold density in figures 1 and 2.

Theoretical curves, generated for comparison of the experimental resistivity data as a function of gold density with predictions of the energylevel model for gold-doped silicon, are also shown in figures 1 and 2. The

curves were derived from calculations based on a solution to the charge

balance equation

n + N^- + + = p + + (1)

where, for the non-degenerate case of interest here:

n « N exp[(F - E )/kT] is the electron density,

p = exp[(E^ - F)/kT] is the hole density,

= 2(27rm^kT/h^) ^'^^ is the density of states in the conduction band,

= 2(27rmj^kT/h^) is the density of states in the valence band,

N

" = N /{I + g exp[(E - F)/kT]} is the ionized (filled) shallow ac3l Q, ^ 3. ceptor (boron, etc.) density,

N

" = N^/{1 + g^ exp[(E_ - F)/kT]} is the ionized (filled) gold-coupled

shallow acceptor density,

\' " ^u''^^

" ^>/^T]{l + gj^ exp[(Ejj - F)/kT]})-l is the

density of negatively ionized gold (filled acceptors)

,

N^"^ = N^/{1 + g^"^ exp[(F - E^)/kT]} is the ionized (empty) shallow

donor (phosphorus, etc.) density,

Njj"^ = N^u^^l + Sd"^ exp[(F - Ejj)/kT]{l + g^-^ exp[(F - E^)/kT]})-l is

the density of positively ionized gold (empty donors),

m^, ffij^ are the electron and hole effective masses,

k is Boltzmann's constant,

T is absolute temperature,

h is Planck's constant,

F is the Fermi energy,

E^, E^ are the energies of the conduction and valence band edges,

N^, Ng, N^^, are the densities of shallow acceptors, gold-coupled

shallow acceptors, gold, and shallow donors,

5
10'

10

10^

E

o

10-

^ 10^

Lii

10

10'

•

/

/

//

/ e

INITIAL RESISTIVITY THEORY EXP. 0.076 12- csn -— o

0.53 £l cm —— A

I.I £l

II £L 20 n

93 n

280 n

1100 a

F300 n

2700 n

cm

} I

/ /

cm —— e cm — A cm —— 0

cm—" • cm A

cm —-—- a cm

•Xr10r2

1013 1014 10,15 1016 1017 GOLD DENSITY (atoms/cm^)

Figure 1. Resistivity as a function of gold density in

boron-doped silicon assuming the degeneracy factor of the

gold donor level to be 8.

6
10-

10 —

10 =

E

o

10 =

^ 10

</) ina:

10

10"

/ /

e' ©

INITIAL RESISTIVITY THEORY EXP. 0.076 n-cm — o

0.53 - ^

I I ^.Qfl) ___

u //

/ /

/ /

i / /

I

II a

20 a93 n

280 i2

1100 a

2300 XI 2700 fl'

cm —

cm —cm —

cm —cm

cm

cm

1015 1016 1017 GOLD DENSITY (atoms/cm^)

Figure 2. Resistivity as a function of gold density in

boron-doped silicon assuming the degeneracy factor of the

gold donor level to be 16.

7
i ^a' ^G* ^A' ^D' degeneracy factors of the shallow acceptor,

^( the gold-coupled shallow acceptor, the gold acceptor, the gold

donor, and the shallow donor, and

E^, Eg, E^, Ejj, E^ are the energies of the shallow acceptor, the goldcoupled shallow acceptor, the gold acceptor, the gold donor, and

the shallow donor.

For the assumed model, shown in figure 3, T = 298 K; Ej) - Ey = 0.35 eV and

Ea - Ev = 0.58 eV [1]; E^, - E^ = 1.111 eV [5], = 1.18 [6], and

= 0.81 m^ [6] (m^ = the free electron mass), so = Vnp = 9.6 x 10^ cm"^.

The lattice mobility [7] and impurity mobility [8] were combined reciprocally

to obtain the carrier mobility used in the calculation of the resistivity.

Also included was the gold-coupled acceptor located at 0.033 eV above the

valence band [3]. Its dependence on gold density is not well established,

but experimental data reported previously [2] suggest that the acceptor density increases approximately as the third power of the gold density with a value of 4.5 x 10^^ cm~^ at a gold density of 1 x 10^^ cm~^. Its degeneracy

factor was taken to be 4, the energy and degeneracy factor of the shallow

acceptor were taken as 0.045 eV and 4, respectively, values appropriate to

boron, and the degeneracy factor of the gold acceptor was taken as Vsi none

of these values enter significantly into the calculation. Various values of

the degeneracy factor for the gold donor were tried to determine which might

give the best fit to the experimental data; results for two values, 8 and 16, are shown in figures 1 and 2, respectively. The densities of the shallow

acceptor were calculated from eq (1) with the assumption that N^^ = 0; values

are listed in table 2.

Although the calculated curves generally fit the experimental data,

there are some deviations which appear to be systematic. Investigations of

two possible sources of the deviations, compensation by donor impurities unintentionally introduced during the gold diffusion and the previously observed

discrepancy between total and electrically active gold [9], have not yet been

completed.

Resistivity vs. Gold Density in n-Type Siliaon — Resistivity measurements were made on phosphorus-doped silicon wafers with initial room- temperature resistivities (before the addition of gold) of 0.30 and 1.0 fi'cm.

The gold density ranged from about 10^^ cm~^ to about 10^'' cm~^. The resistivity of these, and previously measured initially 5.3-, 75-, 380- , and

2300-f2*cm specimens is shown as a function of gold density in figure 4. At

large gold densities, the conductivity type converts from n to p. Specimens

with positive Hall coefficients are plotted with solid symbols in the figure.

For the lower resistivities a sharp increase in resistivity is observed when

the gold density is between one and two times the density of the shallow

donor in agreement with earlier observations [9].

% Theoretical curves, based on the energy-level model described above,

were calculated for each set of data. The theory predicts that the sharp _

The degeneracy factor is defined by Blakemore [4] as referring to the probability that a level contains an electron.
1.111

1.067

>

>-O 0.58

q:

ui

z

liJ 0.35

0.045

••••••

- • • 0

- • • •

• • •••••••••

o o OOOOOO

a: Na„ < b:NA„>N, c: Nau < N,

• • u u • -

• • • •

O O

cI:Nau > N,

Ed

Ev

Figure 3. Energy band diagram at 298 K for silicon doped with gold

and either phosphorus or boron. In this model it is assumed that

the energy differences - E^. and Ep - E^ do not vary with temperature. The energies given for the shallow donor and acceptor levels are appropriate for phosphorus and boron, respectively. No goldcoupled shallow acceptors are shown for cases a and c as their density is negligible when the gold density is less than 10^^ cm~^.

9
Table 2 — Doping Densities of Silicon Crystals

Computed from Measured Resistivity

P--type n--type

a*

-3 cm ^ p ^

, • cm

-3 cm

0.076 2.28 X 1017

0.53 2.59 X 1016 0.30 1.60 X 10 16

1.1 1.18 X iQie 1.0 4.62 X 10 15

11 1.20 X 1015 5.3 8.60 X IQl^

20 6.55 X lOl'^

93 1.40 X lOl*^ 75 6.10 X 10 13

280 4 . /2 X 1013 380

1100 1.18 X 1013

2300 5.76 X 10l2 2300 2.00 X 10l2

2700 4.80 X 10l2

Note — The computed doping densities for low resistivity crystals

(<1 fl'cm) shown above are lower than those obtained experimentally

[Irvin, J. C, Resistivity of Bulk Silicon and of Diffused Layers

in Silicon, Bell System Tech. J. 41, 387-410 (1962)]. This discrepancy arises because of difficulties with the calculation of

ionized impurity and mixed mobilities.

10
10®

10-

10'

E

o

10^

>

/0

I

/

/

/

/ /

/

/

/

/

/

I

I /

10

Q:

10^ -

INITIAL EXP. RESISTIVITY THEORY n p o.30a cm o

1.0 n cm °

5.3 Si m A A

75 XI - cm Q

380 il cm —~ 0 H

2300 a m - 0

10^

10"

10

13 n14 05 J6

lO'"' 10'" 10'" 10

GOLD DENSITY (atoms/cm^)

17

Figure A. Resistivity as a function of gold density in

phosphorus-doped silicon. To the left of the V, the Hall

coefficient is negative; to the right it is positive.

11
increase in resistivity will occur when the gold and shallow donor densities

are equal. Elsewhere, however, the theoretical and experimental plots have

generally similar form. For the curves plotted in figure 4, the energy and

degeneracy factor of the shallow donor were taken as 1,067 eV and Vz* respectively, the degeneracy factor of the gold acceptor was taken as Ve* and the

degeneracy factor of the gold donor was taken as 8, Other parameters were

chosen as described above; values of shallow donor density, calculated as above, are listed in table 2.

To study the effect of changes in the energy of the gold acceptor and

its degeneracy factor on the theoretical fit to the resistivity vs. gold density data of the initially 0.3"f2'cm phosphorus-doped silicon, calculations

were made for several values of the acceptor energy and degeneracy factor.

The results of these calculations are shown in figure 5. Calculations were

made for two energies: 0.54 eV below the conduction band and 0.66 eV above

the valence band. These correspond, respectively, to fixing the level to

the conduction band and to the valence band for a measured activation energy

(energy at 0 K) of 0.54 eV. Because the forbidden energy gap at room temperature is about 1.11 eV rather than about 1.20 eV, fixing the level to the

conduction band edge results in a position lower in the gap, 0,57 eV above

the valence band edge, than fixing it to the valence band edge. In the latter

case, the aoaeptor level is considerably above mid-gap and the increase in re- sistivity at near-equal gold and shallow donor densities is much more gradual

than for the other case considered. For each value of energy, calculations

were made for degeneracy factors of Vz* Ve* and Vsz* Tl^e degeneracy factor

does not affect the position of the sharp rise in resistivity, but it does

influence the resistivity at larger gold density where the Fermi level is

between the gold donor and the gold acceptor. Since neither of these variables affects the position of the sharp increase, another explanation for

the shift must be found before the curves in figure 5 can be fully

interpreted.

A suspected cause of the shift was the presence of a significant quantity

of interstitial gold with electrical characteristics which compensate those

of the substitutional acceptor. To examine the effect of intersitital gold

on the electrical properties of silicon, diffusions of short duration were

done at 950 and 1150°C in both n- and p-type wafers to obtain gold densities

much lower than the saturation value. Electrical measurements were made on the diffused material and the results compared with data obtained on the same or similar starting material which was diffused to saturation for long

times at lower temperatures. The data points for the initially 2300-fi*cm,

n-type silicon at the two lowest gold densities in figure 4 were short-time

diffusions and are either in agreement with nearby points from long-time

diffusions or are close to the calculated curve. In addition, the resistivity data on the p-type silicon diffused for short times were in agreement

with those obtained on other wafers with the same gold density but diffused

for much longer times. Thus the resistivity depends only on the gold density and not on whether saturation was achieved. Schuman [10] studied the

electrical characteristics of silicon diffused with gold for short times and

concluded that interstitial and substitutional gold affect the electrical

properties of silicon in the same manner. The further extension of this

conclusion is that interstitial gold is not responsible for the observed

shift since the electrical properties would be indistinguishable from those

of the substitutional species. This rather surprising similarity need not

12
GOLD DENSITY (atoms/cm^)

Figure 5. Calculated curves of resistivity as a function of gold density for initially 0.3-fi*cin,

phosphorus-doped silicon. The experimental

points are the same as those in figure 4 for the

0.30-fi*cm silicon.

13
be invoked if the rate for the conversion of interstitial to substitutional

gold is very rapid compared to the diffusion time so that the ratio of substitutional to interstitial gold is independent of diffusion time [11]. In

this case, however, the experiment performed cannot discriminate between interstitials and substitutionals since it is not possible to alter their relative densities. At the present time, therefore, it is not possible to rule

out the presence of interstitials as being responsible for the observed

discrepancy.

Activation Energies — Under certain conditions, eq (1) simplifies and

the dominant temperature dependent factor is an exponential which involves

the energy of only a single impurity level. The energy level involved is

determined by the relative densities of the various impurities.

In n-type material with N^^ < N^j (case a, figure 3), the electron density is

N - (N + N ) N. fN ' N^gj expt-(E^ - E^)/kTl, (2)

Au a when n >> p, > N^^ + N^, n << N^^ + and n << N^j - N^^ - N^. This is

the usual activation energy equation for a partially compensated, shallow

donor; it is valid for low temperatures. The Fermi energy is near the shallow donor energy. The density of gold-coupled shallow acceptors under these

conditions is small enough to be neglected.

There are three different energies which can control the majority car- rier density in initially n-type material when N^^ > N^j (case b, figure 3).

When n » p, N<j >> + Nq, n « N^^ + Na + Nq - Nd, and n << - Na - the Fermi energy is near the gold acceptor energy, and the electron density

is

N , - N - N

n » . \ ^ _ . ) N^g^ exp[-(E^ - E^)/kT]. (3)

Au d a G

In this case the energy difference between the gold acceptor and the conduction band edge governs the electron density.

If the gold density is larger, the specimens become p-type (see figure

4) so that p > n. Under this condition, where N^^ >> N^j, + Nq < N^j,

p » n, p << N^j - Ng^ - Nq, and p << N^^ + + Nq - N^, the Fermi energy is near but slightly below the gold acceptor energy, and the hole density is

N, - (N, - N - N^) N

p = \ - N - 1

° r ^=^[-<^A - \>/^^ia a G A

In this case the energy difference between the gold acceptor and the valence

band edge governs the hole density. This is the case depicted in part b of

figure 3.

At still greater gold densities the density of the gold-coupled shallow

acceptor becomes significantly larger so that the condition N^j > N^ + Nq no

longer holds; instead N^j < N^ + Nq and there are no longer enough electrons

14
to populate any of the gold acceptors. When p >> n, p << Na + Ng - N^j, and

p << N^^ + N(j - - Ng, the hole density is

N - (N + N ~ N ) N

a G d °D

In this case the Fermi energy is near the gold donor energy and the energy

difference between the gold donor and the valence band edge governs the hole

density.

In p-type material with N^^ < N^^ (case c, figure 3), the hole density

is

N - (N + N ) N

Au d ^a

when p >> n, Ng. > N^u + N^j, p << N^^ + Nd, and p << - Nau " N^. This is

the usual activation energy equation for a partially compensated, shallow

acceptor; it is valid at low temperatures. The Fermi energy is near the

shallow acceptor energy. Because the density of gold-coupled shallow acceptors is small enough that these levels do not influence the hole density, the

energy difference Eq - does not interfere, and only the energy difference

Ea ~ ^ appears in the expression. Note that the gold donor levels are fully

ionized (contain no electrons) and that, as a result, the gold acceptor

levels do not exist.

In p-type material with N^u > (*^^se d, figure 3), there are two different conditions. In the usual case Nq << N^u so, usually, N^^ > + Nq -

N(j. This is the same condition which led to eq (5); the Fermi energy is near

the gold donor energy and the energy difference between the gold donor and

the valence band edge governs the hole density. If N^u could be reduced such

that N^u < Na + Nq - Nd while >> N^j then the hole density is

N - (N + N.) N

Au d "G

Bruckner [3] found that this condition could be achieved by annealing at

600°C for a short time specimens lightly doped with boron (N^ * 10^^ cm~^)

and diffused with gold at -x^iaOCC (N^u = 10^^ cm"^)

.

From eqs (2) through (7) it can be seen that the slope of the linear

region of a plot of the logarithm of the majority carrier density, corrected

for the temperature dependence of the density of states, Ny or N^,, against

reciprocal temperature is proportional to the energy difference between the

dominant level and the band edge associated with the majority carrier. The

density of states varies directly with the three-halves power of the temperature, T; in addition, the electron and hole effective masses increase

slightly with the temperature [6].

If the energy difference is a linear function of temperature

AE = AE + 6T,

o

15
where AE© is the value of the energy difference at zero kelvin, the temperature dependent term merely introduces the constant factor. In (3/k) , into

the expression for carrier density. As a result the value of the energy

difference determined from the plot is actually the value linearly extrapolated to zero kelvin. This is called the activation energy.

Activation energies can be obtained from the slopes of the linear portions of either resistivity or Hall coefficient data plotted logarithmically

against the reciprocal of the absolute temperature. The activation energy

from both plots is slightly incorrect. Error in the case of the resistivity

plot arises because the decrease of the mobility with temperature is somewhat

greater than the increase of the density of states. Customarily the Hall

coefficient, Ry, is multiplied by T"'^ to correct for the principal temperature dependence of the density of states. In addition to the effective

mass, the scattering factor also contributes a small temperature dependence

[12]. Both were neglected in the analysis of the data reported here.

The activation energy of the gold acceptor with respect to the conduction band was obtained from measurements of resistivity and Hall coefficient

over the temperature range 200 to 400 K on a specimen of phosphorus-doped

silicon with an initial resistivity of 75 fi'cm and a gold density of

3.6 X 10^^ cm~^. Activation energy plots based on resistivity and Hall co- efficient data are shown in figures 6 and 7, respectively. In each case the

activation energy was calculated from the curves by means of a least squares

analysis [13] for the slopes. The data points included in the analysis are shown by circles; the points excluded because of their deviation from linearity are shown as squares. The results are shown in table 3; the uncertainty given for each activation energy is the square root of the estimated

variance of the slope of the experimental line.

Activation energy values for the gold donor were obtained from measurements of resistivity and Hall coefficient over the temperature range 140 to

320 K on specimens cut from boron-doped silicon wafers with initial resistivity of 20 fi'cm and diffused with gold to obtain gold densities of 3.9 x 10^^,

3.1 X 10^^, and 9.9 x 10^^ cm~^. Activation energy plots based on resistivity and Hall coefficient data are shown in figures 8 and 9, respectively. The

analysis for the activation energies was the same as that used for the gold

acceptor; the results are also listed in table 3. Similar values of activation energy were found from resistivity and Hall coefficient data taken on an initially 1100-fi»cm, boron-doped silicon specimen with a gold density of

1.1 X 10^7 cm-3 (see table 3).

To expose the shallow, gold-coupled acceptor level [3] in order to measure its activation energy, the initially 1100-fi«cm, boron-doped specimen

was annealed for 1 h at 600°C in a helium atmosphere. After annealing, the

room temperature resistivity dropped from 1600 to 14 fi*cm, and the Hall co- efficient, with the assiamption of a unity scattering factor, gave a room

temperature carrier density of 1.2 x 10^^ cm~^, somewhat smaller than the

estimated density of the shallow acceptor. This is not unexpected; Bruckner

[3] found that the shallow acceptor density decreased with annealing, but at

a less rapid rate than the density of the electrically active gold donors.

Because of high contact resistance, the low temperature Hall data showed

considerable scatter, but good resistivity data were obtained over the

16
T(K)

Figure 6. Activation energy plot for the gold acceptor in

phosphorus-doped silicon, based on resistivity data.

17
T{K)

Figure 7. Activation energy plot for the gold acceptor in

phosphorus-doped silicon, based on Hall coefficient data.

18
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19
Figure 8. Activation energy plot for the gold donor in boron-doped

silicon, based on resistivity data.

20
T(K)

17 300 250 200 150

Figure 9. Activation energy plot for the gold donor in boron-doped

silicon, based on Hall coefficient data.

21
T(K)

35 25

Figure 10. Activation energy plot for the shallow,

gold-coupled acceptor in boron-doped silicon, based

on resistivity data.

22
temperature range from 15 to 400 K and are plotted in figure 10 as a function of inverse temperature. An activation energy of 0.0349 ± 0.0001 eV

above the valence band edge was calculated from the slope of the linear portion of the curve between 15 and 45 K by the procedure used for the other

gold levels. This value is in reasonable agreement with the only other re- ported value for this level [3]. More observations of this level by a variety of techniques are needed to determine its origin and to obtain a more

definite value for its activation energy.

Carrier Mobility — Typical Hall mobilities were calculated from the

Hall effect and resistivity data reported above for lightly doped specimens

80N850-304 and 20P950-144, respectively. The electron and hole mobilities,

shown in figure 11, are characteristic of lattice scattering and have a ^-2.2 0 -^-2.6 6 dependence on temperature, respectively. When corrected

for the temperature dependence of the scattering factor, T^**^^ for electrons

and T"*^*^^ for holes [12], the deduced conductivity mobilities have about

the same temperature dependence and are in reasonable agreement with direct

measurements of the drift mobilities [7]. Additional study and analysis of

how the temperature variations of the scattering factors, effective masses,

and mobilities depend on doping density are required before quantitative

comparisons can be made.

Heat Treatment Studies — Heat treatments were conducted on silicon

wafers to study the influence of the high-temperature processing during gold

doping on the electrical properties of the specimens . Heat treatments in

oxygen and argon atmospheres were carried out at 950 °C for 168 h and at

1250°C for 8 h on wafers of float-zoned, n- and p-type silicon with initial

resistivity at room temperature of about 2300 fi*cm. These treatments were

performed in a new quartz tube prior to its use for gold diffusion, with the same heating and quenching procedures used during normal gold diffusions

.

Portions of each wafer were checked for gold density by activation analysis

but none X'^a^ detected at a sensitivity limit of 7 x lO-'-^ cm~^.

Generally, resistivity and conductivity-type changes in the p-type

specimens were consistent with the introduction of compensating donors at a density of 10^^ to 10^^ cm~^. Greater changes occurred at 1250 °C than at

950 °C; at the same temperature, more donors were introduced during heat

treatments in the argon atmosphere than during those in the oxygen atmosphere. The increased resistivity observed in the p-type material suggests

that many of the high resistivity data points in figures 1 and 2, which ex- ceed the values predicted by the theoretical curves of resistivity as a function of gold density, could also have been affected by the donors unintentionally introduced during the gold diffusion.

Measurements on the n-type specimens generally showed little or no re- sistivity change after heat treatment. This result suggests that the donors

introduced lie well below the phosphorus level and thus do not influence the

electrical properties of phosphorus-doped specimens

,

The activation energy of the impurity introduced into the initially ptype specimen heat treated in an argon atmosphere at 1250°C was found from

Hall coefficient data taken in the temperature range 200 to 400 K. After

heat treatment, the specimen had converted to rz-type and had a room temperature resistivity of 3.8 x 10^ J^-cm consistent with the introduction of at

23
4000

3000

«o2

300

T 1

i—I—

r

ELECTRONS

HOLES

,—

,

I I I I 1000

Figure 11. Hall mobility for electrons and for holes

in lightly doped silicon as a function of temperature.

24
least 5 X 10^"^ donors. The activation energy found, about 0.53 eV, Is close

to the value of 0.55 eV reported by Collins and Carlson [14] for the upper

donor level of iron in silicon. Although there is a similarity with the

energy of the gold acceptor, the latter would not result in the observed

conversion from p- to n-type.

Minority carrier lifetime measurements were made by the surface photovoltage method [2] on specimens cut from the wafers in the heat treatment

study and compared with lifetime data obtained on untreated wafers cut from

the same crystals. The reductions in lifetime following heat treatment

ranged from factors of 5 to 500 depending on the specific treatment; at a given time and temperature, heat treatment in argon atmosphere resulted in

a lower lifetime than the same treatment in an oxygen atmosphere. Such re- ductions are consistent with the presence of an efficient recombination

center deep in the forbidden gap.

The results reported above suggest that extremely minute amounts of

iron, introduced during the preparation of wafers for diffusion, are likely

to be responsible for the observed resistivity changes in high resistivity

p-type silicon.

25
26
CARRIER LIFETIME MEASUREMENTS

Surface Photovoltage Method — For reasons discussed previously [2], the

steady-state surface photovoltage (SPV) method was studied extensively in con- nection with application to determining minority carrier lifetime. Determination of lifetime from an SPV measurement requires knowledge of two quantities: the minority carrier diffusion coefficient, which is a function of the

impurity concentration in the specimen, and the photon absorption coefficient

as a function of wavelength in the region used. Diffusion coefficients have

been determined from published data on conductivity and drift mobility [7].

Several sets of absorption coefficient data [2] exist in the literature;

these have been used with varying degrees of success.

For silicon which has not been diffused with gold or otherwise heat

treated, the absorption coefficient data of Dash and Newman [15], obtained on silicon not stress-relieved, have given the most linear fit to the SPV measurements. Such measurements are normally made on specimens which have been

etched to remove a 25-iim thick surface layer. To investigate if a layer of

damaged material might be present in an undiffused specimen which required

Dash and Newman absorption coefficient data to fit the SPV results, measurements were repeated after a second etch to remove an additional SO-ym thick

layer. No significant differences in fit or diffusion length were seen.

For specimens which were diffused to obtain a gold density close to saturation or heat-treated for the same conditions of temperature and time, it was found that the absorption coefficient data of Runyan [16], determined on stress-relieved silicon, gave the best fit to the SPV measurements.

For specimens which were diffused to give a gold density considerably

short of saturation, it was found that neither Dash and Newman nor Runyan

absorption coefficient data gave a good fit to the SPV measurements. Of

other data which were tried, those of Braunstein, et at, [17] gave the best

fit, but the result was far from satisfactory. There was more than a factor

of two variation in the diffusion length obtained from the linear region of

the SPV plots made with the various data. To be certain that the SPV measurements were characteristic of the bulk of the specimen, SPV measurements were

repeated after etching the specimen to remove a lOO-ym thick layer. The re- sults were the same, within experimental error, to those obtained after the

etching during initial specimen preparation in which a layer only 25-ym thick was removed. Apparently such a gold diffusion relieves only a portion of the

stress which is initially present in the slice, whereas diffusions of sufficient

duration to achieve a much larger gold density are adequate to relieve essentially

all of the stress in the slice. These experiments also suggest that the property

of the crystal which affects the absorption coefficient is characteristic of the

bulk material rather than of a surface layer.

To obtain absorption coefficient data appropriate to the heat treatments

given the material in this study, optical transmission measurements are underway. The wavelength range used for the SPV measurements in silicon is from

about 0.8 to 1.1 ym in the vicinity of the band gap absorption edge. In this

range the absorption coefficient changes rapidly from a value of about 1000 cm~^

at 0.8 ym to about 10 cm~^ at 1.1 ym. A very thin specimen is needed to obtain

accurate transmission measurements when the absorption coefficient is high and

27
thicker ones are required at wavelengths with less absorption. To cover the

wavelength range, four chetn-mechanically polished silicon wafers were prepared

with thicknesses of about 30, 100, 300, and 1000 ym. Measurements have been

made on the wafers and they have been heat treated at a temperature and time

used for a gold diffusion in preparation for the second set of measurements.

A series of SPV measurements was made on Hall bars cut from boron-doped

silicon wafers with gold densitites from 5 x 10^^+ to 5 X iQlS cm ^. These

densities were much less than those of the shallow Impurity in the specimens

studied. Hence the added gold results in little increase in the resistivity

but may give rise to large reductions in the carrier lifetime. The measured

diffusion lengths for these specimens ranged from 1 to 10 um. The lifetime

results plotted against gold density showed considerable scatter which could

be attributed to a random variation of about ±2 ym in the measured diffusion

length. Numerous repetitive measurements on the same specimen confirmed the

presence of these random variations. It thus appears that increased control

over experimental conditions is necessary to obtain data from which a reliable value of capture cross section can be calculated. Although several improvements in the SPV apparatus and measurement procedures were instituted,

it has not yet been possible to reduce the variability to the desired level

to permit useful measurements on material with lifetime down to a few nanoseconds.

In a related task area, work was completed on an analysis of SPV measurements in epitaxial layers. The report of this work is included as Appendix C.

Diode Recovery Methods — Because of the difficulties and delays in

applying the SPV method to the measurement of short diffusion lengths, attention was redirected toward various diode recovery methods. The work undertaken focused on two test methods which are commonly used to determine minority carrier lifetime: reverse recovery (RR) and open circuit voltage decay

(OCVD) . The evaluation and development of neither method has been completed;

consequently, the following sections cover initial efforts which have been

directed toward a better understanding of the methods in preparation for

applying them to measurements on gold-doped specimens with short lifetime.

Although both RR and OCVD have gained general acceptance as techniques

for determining minority carrier lifetime, there is poor correlation in the

minority carrier lifetime computed from the two experiments for the same

diode. The results of Basset t and Hogarth [18] and Kao and Davis [19] showed

that the minority carrier lifetime, as computed from OCVD and RR experiments

and other different experiments, often differed by as much as a factor of 2 to 3. Measurements made in this laboratory on a randomly chosen diode showed

that the minority carrier lifetime for this diode as computed from RR and

OCVD experiments differed by a factor of roughly 2.5. The thrust of the ana- lytical and experimental work reported in the following sections was to evaluate the RR and OCVD experiments to find out why the lifetimes computed from

these experiments often did not agree, and to determine under what circumstances the computed lifetimes could be made to agree.

The devices studied in the RR and OCVD experiments to date have been

p-n diodes; these devices were selected because of their simplicity. To

28
If

-Ir

TIME

Figure 12. Idealized reverse recovery transient.

make the analysis tractable the following assumptions were made in developing expressions to relate lifetime to the RR and OCVD transients:

1. The p-n junction was assumed to be abrupt.

2. The doping level on one side of the junction was assumed to be much

greater than the other side so that only minority carriers in the

neutral region of the lightly doped side of the junction had to be

considered.

3. The device was assumed to have recombination-type contacts so that

the excess carrier density at the contacts was zero.

An important variable in the discussion which follows is the width of

the neutral region on the lightly doped side of the p-n junction; in the literature this is referred to as the diode base width, W. The important parameter in the theory is the ratio of W to the minority carrier diffusion

length, L; in the following, a diode whose base width is shorter than 3 to

5 times the diffusion length is called a short base diode.

Eeverse Recovery Method — A RR transient is observed whenever a p-n

junction which has been forward biased for a sufficiently long time is suddenly reverse biased. An idealized wave form is shown in figure 12. Initially the diode is forward biased and conducting a current, If; when the

bias is abruptly reversed the diode conducts a constant current, Ij,, for a time, tg, called the storage time. At the time tg after the reversal, the

minority carrier density at the interface between the space charge region

and the neutral region on the lightly doped side of the junction is equal

to the equilibrium minority carrier density in the neutral region. At the same time, it is observed experimentally that the voltage across the

29
junction is zero. Throughout the recovery phase of the transient which tollows, the space charge region depletes, and the current decays to its re- verse leakage value. Another time that is referred to in the literature is

the recovery time, tj-; this is the time interval between the time the diode

is reverse biased to the time required for the reverse current to decay to

10 percent of its initial value.

The possibility of using the reverse recovery transient to determine

the lifetime of the minority carriers associated with a device was first investigated by Pell [20]. Kingston [21] used an approximate approach to

develop a relation between the ratio of the minority carrier lifetime x and

the storage time and the ratio of the forward and reverse currents for a diode whose base width was infinitely long; he showed that

erf 1 +^

-1

(9)

Lax and Neustadter [22] derived eq (9) rigorously. Byczkowski and Madigan

[23] extended Lax and Neustadter 's analysis to the case of diodes with arbitrary base width; they showed that

t

exp |-[1 + (n + w

n=0

2, 2. 1 + (n + |) (7T ^)

1-1

r

W ^ W — tanh rLi Li (10)

To investigate the applicability of these relationships, reverse re- covery experiments were conducted in two ways

:

1. The forward current was fixed at some value, generally 20 mA,

and t was measured as a function of I . s r

2. Both the forward and reverse currents were varied such the

ratio If/Ij- was constant and t was measured as a function

of I . ® r The results of the first type of RR experiment showed that the storage times

of some diodes varied logarithmically with the forward to reverse current

ratio

(11)

Subsequent experiments showed that the data for some diodes could be fitted

with eq (11), for example see figure 13, but that data for other diodes could

be fitted with eq (9), see figure 14.

Grove and Sah [24] have shown that tg should vary logarithmically with

(1 + If/Ir) when W/L << 1 and If/Ir >> 1. This result suggested that tg

varied logarithmically with (1 + If/I^) because the base widths of the diodes

were less than or roughly equal to the diffusion length of the minority

30
1+If/Ir

Figure 13. Reverse recovery characteristics of a short

base diode. The solid line is calculated from eq (11);

experimental points are shown as open circles.

Hlf/Ir

Figure 14. Reverse recovery characteristics of a long

base diode. Experimental points are shown as open circles; the solid curves were calculated from eq (9) for

two values of t. For this example, the scatter in the

data results in a ±1 ys uncertainty in t. 31
carriers. An examination of the dimensions of the diodes which obeyed eq (11)

showed they were short base diodes. Also, a check of several diodes which

obeyed eq (9) showed that they were long base diodes.

The different functional dependences of ts on If/Ir ^or a short and long

base diodes provides a means to determine whether a particular diode can be

characterized as a long or short base diode. If eq (9), with the appropriate

choice of t fits the RR data, the diode can be assumed to be a long base

diode; however, if the fit cannot be made and if tg varies logarithmically

with (1 + If/Ij-), the diode can be considered to be a short base diode.

To study further the effect of diode base width on the RE. transient,

eq (10) was evaluated for various base widths; the results of these calculations are shown in figure 15. The calculations show that for W/L > 3 and

If/Ij- < 10, less than 2.5 percent error is introduced in using eq (9) to

calculate the minority carrier lifetime rather than eq (10); however, if Lax

and Neustadter's expression were used to compute the lifetime in a short base

diode (W/L < 3), the computed lifetime could be significantly in error.

The results of the second type of RR experiment showed that if If and

Ij- were varied so that the ratio of If/Ij- was constant, the storage time

changed. For five of the eight types of diodes which have been tested, tg

decreased when If increased; for the remaining three types of diodes tg increased. This effect was studied by Owen and Wilkinson [25] who attributed

it to saturable traps, but it is not certain at the present time this represents a complete explanation.

Open-Circuit Voltage Decay Method — If a forward biased p-n junction

is suddenly open circuited, the initial part of the voltage decay transient

is often observed to decay linearly with time. An idealized transient is

shown in figure 16, Lederhandler and Giacoletto [26] concluded that the

slope of the linear part of the voltage decay transient (dV/dt) was related

to an effective minority carrier lifetime, t , by the relation

(12)

where k is Boltzmann's constant, T is absolute temperature, and q is the

electronic charge. Subsequent authors have developed and applied his technique to -p-n and p~i-n diodes. Bassett [27] showed that the non-linear variations in the voltage decay which are generally observed at the end of the

OCVD transient were due to surface effects. Choo and Mazur [28] developed a general expression for the decay of mobile charge carriers in a p-n diode of

arbitrary width. From their analysis and experimental results it can be inferred that for short base width, the geometry must be considered in calculating the lifetime for the decay transient.

The results of the OCVD experiments to date indicate that the slope of

the linear portion of the OCVD transient is independent of current level.

Also, it was noted that when a diode was shunted with a resistor, the duration of the OCVD transient is shortened, but the slope of the linear part

of the voltage decay is unaffected. Throughout all of the OCVD experiments

a more or less linear voltage decay transient was always observed.

32
Figure 15. Diode storage time (tg) normalized to lifetime

(x) as a function of forward-to-reverse current ratio

(If /Ij.) calculated from eq (10) . The curve for W/L > 5 is

identical with eq (9)

.

TIME

Figure 16. Idealized open circuit voltage decay transient.

33
Comparisons Between RR and OCVD Measurements — The discussion above has

focused on the problems encountered in correlating the lifetime computed

from RR and OCVD experiments on short base diodes. The difficulties in cor- relating the minority carrier lifetimes associated with long base diodes were

much less. A comparison of the lifetimes computed from RR and OCVD experiments on diodes for which the RR transient obeyed eq (9) showed that the minority carrier lifetime for a particular device agreed to within ±10 percent

of the mean of the two values if a factor of 2 is included on the right-hand

side of eq (12) as suggested by Choo and Mazur [28] for high injection in

n"^p diodes. RR measurements were made with a forward current of 20 mA. OCVD

measurements, which were found not to depend greatly on current level, were

generally made with a forward current of 20 mA or more. Since the experimental error in the measurement of If, I^, tg, and dV/dt was at least ±5 percent,

the experimentally determined correlation of ±10 percent was considered to be

quite satisfactory. For short base diodes the agreement is not yet this

close.

34
DIRECTIONS FOR FUTURE WORK

More complete characterization of the gold-coupled shallow acceptor and

an explanation for the apparent difference between electrically active and

total gold densities are required to elucidate the energy level model for

gold in silicon.

The next phases of the work involve the study of gold-doped p'^n and n'^p

junctions. Fabrication procedures are being developed. These junctions will

be used to study, first., the uniformity of gold doping in the vicinity of the

junction and, second, the recombination characteristics of the gold centers.

The first study will be carried out by using capacitance-voltage and spreading resistance measurements. The second will involve stimulated current and

capacitance measurements in addition to RR and OCVD lifetime measurements.

Also, these junctions will be useful in studying the dependence of reverse

recovery storage time on the magnitude of the current for a constant ratio of

If to Ij..

35
36
REFERENCES

1. Collins, C. B„, Carlson, R. 0., and Gallagher, C. J., Properties of

Gold-Doped Silicon, Fhys. Rev, 105 , 1168-1173 (1957).

2. Thurber, W. R. , and Bullis, W. M. , Resistivity and Carrier Lifetime in

Gold-Doped Silicon, Air Force Cambridge Research Laboratories Report

AFCRL-72-0076 (January 31, 1972). Available from National Technical

Information Service, Springfield, Virginia 22151, Accession Number

AD 740592.

3. Bruckner, B, , Electrical Properties of Gold-Doped Silicon, Phys. Status

Solidi A 4_, 685-692 (1971)

.

4. Blakemore, J. S., Semiconductor Statistics, pp. 118-120 (Pergamon Press,

New York, 1962)

,

5. Macfarlane, G. G. , McLean, T. P., Quarrington, J. E., and Roberts, V.,

Fine Structure in the Absorption-Edge Spectrum of Si, Phys. Rev. Ill , 1245-1254 (1958).

6. Barber, H. D., Effective Mass and Intrinsic Concentration in Silicon,

Solid-state Electronics 10, 1039-1051 (1967).

7. Ludwig, G. W. , and Watters, R. L. , Drift and Conductivity Mobility in

Silicon, Phys. Rev, 101 , 1699-1701 (1956).

8. Brooks, H. , Theory of the Electrical Properties of Germanium and Silicon, Advances in Electronics and Electron Physics^ Vol. VII, L. Marton,

ed. , pp. 156-160. (Academic Press, New York, 1955).

9. Bullis, W. M. , and Strieter, F. J., Electrical Properties of n-Type

Silicon Doped with Gold, J. Appl. Phys. 3i9, 314-318 (1968).

10. Schuman, V. B. , Diffusion of Gold in Silicon, Soviet Phys. Semiconductors

1, 790-791 (1967-68).

11. Brotherton, S. D., and Rogers, T^ L., Influence of Dislocations on Gold

Diffusion into Thin Silicon Slices, Solid-State Electronics 15 , 853-860

(1972),

12. Messier, J., and Flores, J. M. , Temperature Dependence of Hall Mobility

and Ug/yjj for Si, J. Phys. Chem. Solids 24., 1539-1542 (1963).

13. Natrella, M. G. , Experimental Statistics, NBS Handbook 91 (August 1,

1963), 115-5.1.3.

14. Collins, C. B., and Carlson, R. 0., Properties of Silicon Doped with

Iron or Copper, Phys. Rev. 108 , 1409-1414 (1957).

15. Dash, W. C. , and Newman, R. , Intrinsic Optical Absorption in SingleCrystal Germanium and Silicon at 77°K and 300°K, Phys. Rev. 99, 1151-

1155 (1955).

37
16. Runyan, W. R, , A Study of the Absorption Coefficient of Silicon in the

Wave Length Region between 0.5 and 1.1 Micron, Southern Methodist University Report SMU 83-13 (1967). Available from National Technical

Information Service, Springfield, Virginia 22151, Accession Number

N68- 16510.

17. Braunstein, R. , Moore, A. R, , and Herman, F., Intrinsic Optical Absorption in Germanium-Silicon Alloys, Phys. Rev. 109, 695-710 (1958).

18. Bassett, R. J., and Hogarth, C. A., A Direct Comparison Between Three

Different Methods of Measuring the Minority Carrier Lifetime in Thin

Silicon Slices, Int. J. Eleotronios 25, 585-590 (1968).

19. Kao, Y, C. , and Davis, J. R. , Correlations Between Reverse Recovery

Time and Lifetime of p-n Junction Driven by a Current Ramp, IEEE Trans.

Electron Devices ED-17 , 652-657 (1970).

20. Pell, E. M. , Recombination Rate in Germanium by Observation of Pulsed

Reverse Characteristic, Phys. Rev. 90_, 278-279 (1953),

21. Kingston, R, H. , Switching Time in Junction Diodes and Junction Transistors, Proa. IRE hl^y 829-834 (1954).

22. Lax, B. , and Neustadter, S, F., Transient Response of a p-n Junction,

J. Appl. Phys. 25_, 1148-1154 (1954).

23. Byczkowski, M. , and Madigan, J. R, , Minority Carrier Lifetime in p-n

Junction Devices, J. Appl. Phys. 28, 878-881 (1957).

24. Grove, A. S,, and Sah, C. T. , Simple Analytical Approximations to the

Switching Times in Narrow Base Diodes, Solid-State Electronics 7_, 107-

110 (1964).

25. Owen, D. B. B. , and Wilkinson, E. L. G., Junction Recovery and Trapping

in Silicon p'^-n Junctions, Int. J. Electronics 20, 21-29 (1966).

26. Lederhandler , S. R, , and Giacoletto, L. J., Measurement of Minority

Carrier Lifetime and Surface Effects in Junction Devices, Proa. IRE

43, 477-483 (1955).

27. Bassett, R. J., Observations on a Method of Determining the Carrier

Lifetime in p+-y-n+ Diodes, Solid-State Electronics 12, 385-391 (1969).

28. Choo, S. C, and Mazur, R. G., Open Circuit Voltage Decay Behavior of

Junction Devices, Solid-State Electronics 13 , 553-564 (1970).

38
APPENDIX A

SPECIMEN PREPARATION

Wafers were cut from single crystals of silicon with a diamond saw and

lapped to a final thickness of about 1.1 mm with 12-ym alumina. The resistivity of representative wafers was measured by the four-probe [1] or van der

Pauw [2] method. To test for radial homogeneity of the shallow doping impurities, the resistivity profile was measured by the four-probe method on one or more wafers from each crystal. After completion of the initial resistivity

measurements, both sides of each wafer were chem-mechanically polished [3]

in preparation for the gold diffusion.

Immediately prior to insertion in the diffusion furnace, the wafers were

cleaned and plated with gold. The cleaning procedure consisted of the following steps: ultrasonic agitation in detergent for one minute, rinses in distilled water and methanol, ultrasonic agitation in trichloroethylene for one

minute, rinse in methanol, ultrasonic agitation in methanol, soaking in

chromic acid for at least one minute, rinses in distilled water and methanol,

three rinses in nitric acid of one minute each, rinses in distilled water and

methanol, soaking in hydrofluoric acid for one minute, and final rinses in

distilled water and methanol. A 40-nm thick layer of gold was then evaporated

on both sides of the wafer and the wafer was loaded into the quartz tube of

the diffusion furnace.

Diffusion took place in an open-tube system. Most of the diffusions were

done in an atmosphere of high-purity oxygen, which flowed through the quartz

diffusion tube at a rate of 4 x 10~^ m^/s. Diffusions were generally made at

temperatures of 850, 950, 1050, 1150, and 1250°C, although other temperatures

were also used when more closely spaced values of gold density were desired.

Diffusion times varied from 2 weeks at 850''C to 8 hours at 1250°C. The wafers

were quenched by pulling them to the cool end of the diffusion tube and then

placing them on an aluminum block.

To estimate the uniformity of the gold as a function of depth, spreading

resistance measurements were made on portions of a gold-diffused wafer. The

starting material was l.l-J^-cm, boron-doped silicon; a companion wafer diffused at the same time had a final resistivity of 2.1 fi*cm and a gold density

of 5.1 X 10-^^ cm""^. A portion of the wafer was lapped at an angle of 5 deg

43 min to study the uniformity through more than half the wafer thickness and

another portion was lapped at an angle of 1 deg 9 min to obtain more resolution in the region close to the wafer surface. Two-probe spreading resistance measurements were made on the angle-lapped portions by an apparatus

which automatically stepped the probes and recorded the data. The resulting

plots showed that the resistance was constant in the center region and that

the expected increase in resistance due to excess gold occurred only within

15 to 20 ym from the wafer surface. To eliminate gold in the surface regions, each side of the wafer was lapped to remove a 125-um thick layer before

any measurements were made.

Hall bars with four side arms and expanded ends designed to meet the

specifications of the standard method for Hall effect measurements [2] were

cut ultrasonically from the lapped wafers for electrical measurements.

39
Aluminum contact pads were evaporated on one surface of the side arms and

ends. Pressure contact to the aluminum pads was made with flat phosphorbronze springs and the measurements x^^re made in a light-tight holder. Some

early data were obtained at room-temperature (25 ± 1°C) equilibrium whereas

more recent measurements have been made with the temperature maintained at

24.8 ± 0.1°C by a temperature control system. The latter method has proved

superior in that drifts in the resistivity with time are no longer present.

REFERENCES

1. Standard Method for Measuring Resistivity of Silicon Slices with a Collinear Four-Probe Array (ASTM Designation: F84-72), Annual Book of

ASTM Standards^ Part 8 (American Society for Testing and Materials,

Philadelphia, 1972).

2. Standard Method for Measuring Hall Mobility in Extrinsic Semiconductor

Single Crystals (ASTM Designation: F76-72) , Annual Book of ASTM Standardsj Part 8 (American Society for Testing and Materials, Philadelphia,

1972).

3. Buehler, M, G., Peripheral and Diffused Layer Effects on Doping Profiles,

IEEE Trans. Electron Devices^ ED-19 , 1171-1178 (1972) . (Patent)

40
APPENDIX B

ACTIVATION ANALYSIS

For the analysis of gold density a disc was cut ultrasonically from the

remainder of the wafer. The density was determined by neutron activation

analysis using the following procedure. The silicon specimens and standard

were encapsulated in polyethylene vials and irradiated for either 30 or

60 min at a neutron flux of 1 to 6 x 10^^ cm~^*s~-^. Copper foils were attached to each specimen and to the standard to normalize for flux variation.

The standard consisted of a filter paper approximately the shape and size of

the silicon specimens on which was pipetted a known solution of gold in aqua

regia. After irradiation the specimens were allowed to decay for two to four

days to minimize short-lived Interferences and then counted using a lithiumdrifted germanixim gamma -ray detector in conjunction with a multi-channel

analyzer. The results were calculated using the standard-comparator method.

41
42
APPENDIX C

Solid-Sltilc Electronics 1972, Vol. 15, pp. 1097-1102. Pergamon Press. Printed in Great Britain

INTERPRETATION OF STEADY-STATE SURFACE

PHOTOVOLTAGE MEASUREMENTS IN

EPITAXIAL SEMICONDUCTOR LAYERS

W. E. PHILLIPS

Institute for Applied Technology, National Bureau of Standards, Washington, D.C. 20234, U.S.A.

{Received 24 January \ 912\ in revisedform M April 1972)

Abstract- Analysis of the steady-state surface photovoltage (SPV) method of measuring minority

carrier diffusion length (L) has been extended to the case of an epitaxial layer on a thick substrate. In layers with thickness greater than four diffusion lengths, the measurement yields the bulk value of L. For layers thinner than 0.5L, the measured value is that of the substrate. For intermediate thick- nesses, the bulk value of L can be estimated. The method also provides a sensitive means of observing

the influence of surface conditions on the absorption characteristics of silicon.

NOTATION

A, B, C boundary condition constants (m"^) Ao, Bo functions defined by equations 1 0 and 1

1

d thickness of epitaxial layer (m)

D minority carrier diffusion coefficient (m^sec)

lo photon intensity at front surface of specimen

(sec"'m~^) k Boitzmann's constant (J °K"') L bulk diffusion length (m)

Lo effective diffusion length or SPV intercept value (m)

p(x) excess minority carrier density at x (m~^)

Po equilibrium minority carrier density in the substrate (m~^) q electronic charge (C) Q function defined by equation (8) R reflectance of the front surface ^0 ratio defined by equation ( 12)

i surface recombination velocity at front surface of specimen (m/sec) T temperature {°K)

V bias voltage across junction (V)

Fspv amplitude of the SPV signal (V) X distance measured from front surface under

native oxide (m)

Xo value of a"' at which Taylor expansion is made (m) a absorption coeflficient (m"') y quantum efficiency (carrier pair/quantum)

4> built-in (self-diffusion) junction potential (V)

T bulk minority carrier lifetime (sec) Subscript! refers to front region (epitaxial layer) Subscript 2 refers to substrate region

The increasing use and sophistication of devices

made of epitaxial semiconductor materials has increased the need for characterization parameters

for such materials. The steady-state surface photovoltage (SPV) method is capable of measuring

bulk minority carrier diffusion lengths under the surface and by a suitable choice of wavelengths

the measurement can be confined to thin regions

such as epitaxial layers. The measurement is also independent of surface conditions; however, as is discussed below, the type of surface must be

considered in the choice of appropriate absorption

coefficients. Analysis of the SPV method has been extended

to the case of an extrinsic epitaxial layer on a thick substrate of the same conductivity type with an

equal or shorter diffusion length. It appears that the SPV method is suitable for measuring diffusion length or carrier lifetime in the epitaxial layer for material in which the diffusion length is less than about a quarter of the thickness of the epitaxial

layer. For epitaxial material in which the effective diffusion length, Lo, is greater than twice the

epitaxial layer thickness, the method measures

substrate diffusion length. For epitaxial thicknesses

in the range between 0.5 Lq and 4Lo, a knowledge

of the substrate diffusion length, impurity concentrations, and epitaxial layer thickness permits a determination of the diffusion length in the

epitaxial layer.

SPV measurements in thick specimens have

been analyzed by Goodman[l] and by Bergmann,

Fritzsche, and Riccius[2] with the assumptions

that the diffusion length and the reciprocal absorption coefficient are much less than the specimen

43
W. E. PHILLIPS

thickness and much greater than the depth of the surface space-charge region. The material is assumed to be extrinsic and the excess carrier density small compared to the majority carrier thermal equilibrium density. Trapping was neglected. Under these conditions, the surface photovoltage is a function of the excess minority

charge density injected into the surface space- charge layer. If small variations in quantum

efficiency and reflectance with wavelength are neglected, the incident light intensity, /q, required

to produce a given SPV, Vsw, is a linear function of reciprocal absorption coefficient, a"':

/o = constant (a ' + L) (i:

The plot of /„ against a"' has an extrapolated

intercept for /o = 0 at a"' = — L. For thin layers such as epitaxial layers, the condition that the diffusion length be much less than the thickness may not be met. However,

even when the condition was not met, experimental

SPV plots of /o against a"' still were found to yield a straight line. The present analysis was undertaken

in order to investigate this experimental result. A mathematical model was developed by adding

a region to represent the epitaxial layer, which may

be thin, in front of a region to represent the

substrate, assumed to be thick compared to the

diffusion length. Trapping effects were again

omitted since Choo and Sanderson [3] have shown

that majority trapping and moderate minority

trapping do not influence the SPV measurement

at the low injection levels which are appropriate

for the method.

The steady-state current continuity equation was

solved to obtain the excess minority carrier density

in both regions, Px{x) and Pzix). Under the conditions for which a one-dimensional analysis is valid and for small electric fields, the solution in the epitaxial layer is:*

y/o(i-/?)aT.e-"^

(2)

and the solution in the thick substrate is:

*Sawyer and Rediker[4] showed that this type function remains well behaved at aL, (or aL>) = \. The

solution then is the same except that the last term becomes 0.5 y/„(l - R)(x^XTe'-''^

.

-y/o(l -/?)aT2e-"-^

(3)

The constants A, B, and C are evaluated from

the front surface recombination velocity of the

epitaxial layer, the continuity of current across the

epitaxial-substrate junction, and the potential difference across the junction. At the front surface, = 0,

D,dpJ(bc = sp,. (4)

The continuity of minority carrier current across

the epitaxial-substrate junction yields the equation

at A' = d:

dp, dp2

dx Di dx

(5)

Generalized boundary conditions for semiconductor junctions have been derived by Harrick

[5] and Fletcher[6]. For heavily doped substrates of the same conductivity type (n on or p on

their equations simplify to the condition:

p.(d) =pAd)t-"^"'^' + p^qVlkT. (6)

Because the signal is extracted through a capacitance, the bias voltage, F, is essentially zero. With

K = 0 and a highly doped substrate, the Fermi level

40 60 80

Fig. 1 . Theoretical photon intensity required to produce a given SPV response as a function of reciprocal absorption coefficients for various diffusion lengths and a speci- men thickness of 10 /xm. See text for meaning of data

points.

44
STEADY-STATE SURFACE PHOTOVOLTAGE

is near the band edge in both the substrate and the junction region so that recombination in the space-charge region need not be distinguished

from substrate recombination.

Subject to the boundary conditions of equations

(4)-(6), and the previously assumed conditions [2], except for the relaxation of the thickness condition

d > L, the constants A, B, and C can be tediously but straightforwardly evaluated for a constant

Po(0) which corresponds to a given Kspv The

resultant equation is then solved for the photon

intensity required to produce the given Fypv as:

_ p,(0) ( ]-a^LA .{. .d ^ .d

1q — — 777^1 ]Q —\smh- Q:L,cosh —

y{\-R)T^\ a

+ ^e-'*'*'-(cosh^-aL, sinh^

+ 2e- D.I . -q<blkT . it-'--)

:- 1

(7)

where

Q = sinh -^ + ^

cosh /+ ^e-**"^^

, , d , sLi . , d

X ( cosh —+ sinh — .. (8)

A plot of Iq (in arbitrary units)* against a"' is shown in Fig. 1 for various epitaxial layer diffusion lengths and for an epitaxial layer thickness of 10

/u,m, a substrate diffusion length of 2.5 ju,m, and a

built-in junction potential of 160 mV which would

be expected for the material described in the next paragraph. The relationship is seen to be nearly

linear. The experimental values of intensity shown in Fig. 1 were measured by the procedure given in the Appendix and are for a 5 fl cm «-type silicon layer 10 ^im thick on a 0.009511 cm antimonydoped (111) substrate 250 p,m thick. Those

*At short diffusion lengths the variation with wavelength in the term (1 — R) becomes important so that the quantity actually plotted is /„(! — R) as described in the Appendix. Without the correction L„ would be 5.2 /xm

instead of 5.0 ju,m.

experimental values of intensity identified by

circles are plotted against the reciprocal absorption

coefficients of Runyan[7J and the same values

identified by squares are plotted against the

reciprocal absorption coefficients of Dash and

Newman[8]. When Runyan's coefficients are used,

the experimental points produce a straight line

in agreement with the theory. When the points

are plotted against the coefficients of Dash and

Newman, a straight line is not obtained. The difference in absorption coefficients may

be due to surface stresses in the silicon single

crystals used by Dash and Newman. The Runyan

coefficients were determined in stress-relieved

epitaxial silicon. To test this hypothesis, SPV data from a single crystal specimen with a lapped

surface were plotted against both sets of coefficients. The linear plot was that against Dash

and Newman coefficients. The surface of the specimen was polished with a cupric ion chemicalmechanical treatment [9] and the SPV data were

retaken and the plots redone. The linear plot was

then obtained for the Runyan coefficients. The

intercept values of both linear plots were in good

agreement. From this it was concluded that the Runyan coefficients are appropriate for the experimental data in Fig. 1. The linearity of the theoretical SPV plot was

further investigated by making a Taylor series expansion of /„ about the point a"^ = x„. The

intercept, Lo, was calculated as:

(9)

where

/lo = Xf, smh 7 L, cosh -—h --^-i e^"*'*^

X (^Xocosh^-L, sinh^j-i-2L,i?oe"'"-^'' (10)

Bn — 2Xn Xo^xnh- L, cosh I

^-^q-qI'Ikt

L] L] O1L2

X ^jc„ cosh^

Li sinh^^ + 4AoL,/?oe-'"-^''

(V - ) ( sinh ^+^4^ e^«*'*-^ cosh f45
W. E. PHILLIPS

+ - ^1 -1

(11

and

Q<t>lkT

A plot of the diffusion length in the epitaxial layer

normalized to the intercept value, Ly, against the

epitaxial layer thickness, d, also normalized to

units of the intercept value, is shown in Fig. 2 for various ratios of epitaxial layer to substrate

diffusion lengths, LJL-,, and for d^lOfxm and

X(,= l50fjim. The same quantities are shown in Fig. 3 for various ratios of Lold. Other values of

Xo > 20 fxm give the same results. For values of

L-i > d, values of L, < are not plotted since they

violate the boundary conditions assumed.

It can be seen from both Figs. 2 and 3 that for specimens of thickness greater than about four

diffusion lengths, the effective diffusion length, Lo, as given by the (negative) intercept is the bulk

diffusion length (i.e., L,/Lu = 1). This conclusion

is in agreement with the results for thick specimens

200

oioo

50- <a 20 X

l-O 10'

1 L| nOOL^

1

^ = 160 mV'""^

d= lO/im

L.'IOLe '

-

^ =160mV \

<i> =0

1 1

5-

2

-

I 10 THICKNESS RATIO d/Lo

100

Fig. 2. Calculated SPV minority carrier diffusion length

in an epitaxial layer as a function of layer thickness, both normalized to SPV intercept length, for various fixed

ratios of Z., toL,.

previously reported[l, 2]. For thin epitaxial layers

with djLo < 0.5, the intercept value is independent

of the epitaxial layer bulk diffusion length L,, but

is the diffusion length of the substrate. Inter- mediate values of d/Lg lie in a transition region. For the interpretation of values of Lq in the

transition region, 0.5L„ < d < 4Lo, a plot like Fig.

3 with appropriate values of L2 and ({) is useful. Higher junction potentials, (/>, converge the curves

for d/Li > 2 upon the d/Lg = 2 coordinate. The

diffusion length ratio corresponding to the appropriate value of dILg is the multiplicative correction

factor to convert the effective diffusion length to

olOO

50-

.20 IH 10 z

UJ 5 o

it

' a

0.5

1 1 1 1 1

1

d = lOftm _ ^=160mV

d/L,=10* — d/Lj=10'

CM

in CM IT) d/Lj=10' d

0

d

d d d

in — d/L, =10

-J _J

_j*

T3 0

V1

1 L :1

1

1 1 1 1 0.01 0.02 005 01 0.2 as 1 2 5 THICKNESS RATIO d/U

10 20 50

Fig. 3. Same as Fig. 2 except for various fixed ratios of d to L-z46
STEADY-STATE SURFACE PHOTOVOLTAGE

the bulk diflFusion length. For example, the expei i- mental measurement shown in Fig. I indicates an Lo of about 5 fim. An SPV measurement on the back surface of the specimen yielded a value of

2.5 /xm for L.. Since dlL„ = 2 and d/L.^ = 4, Fig. 3 can be interpolated to give a value of L,/L,i very

nearly unity so that L, = L,, = 5 /xm. This value confirms the theoretical result shown in Fig. 1. The independence of L,, on L, when ^//L„ < 0.5 can be explained by considering the interface to be

an imperfectly reflective boundary so that the image of the front surface acts as a carrier sink which limits the effective diffusion length under

such conditions. However, in the SPV method,

the excess minority carrier density at the front surface is kept constant so that the surface re- combination should not play a role in the measurement. This behavior is supported by the fact that the surface recombination velocity s cancels for

all values of s in equation (9) and appears in equation (7) only in Q which affects the arbitrary

amplitude of the SPV plot. Since the surface recombination is held constant, then one is able

to see the effects of carrier leakage through the

interface which is dependent upon the substrate

diffusion length. However, the surface recombination velocity can be varied to improve sensitivity

through the amplitude dependency. The analysis

indicates that the optimum value for s is near DJL^.

Demands upon the precision of the measure- ments increase for shorter diffusion lengths. The

precision can be improved by making additional measurements at intermediate wavelengths.

It can be concluded from this work that the SPV

method is suitable for measuring effective carrier diffusion lengths. When the epitaxial layer is four or more diffusion lengths in thickness, the measured

value is the bulk diffusion length of the epitaxial material. When the epitaxial layer is thinner than

about four diffusion lengths, the measured value of

diffusion length is an effective value which also depends upon the substrate diffusion length.

This limitation on diffusion length measure- ments in thin layers was also found by Byczkowski

and Madigan[10] on measuring carrier lifetime in p-n junction devices by the reverse recovery method. They found that for base width greater than three diffusion lengths, the recovery time is proportional to the carrier lifetime; but for base

widths less than one diffusion length, the ratio of recovery time to carrier lifetime is proportional to

the square of the ratio of the base width to diffusion

length. This can be restated as the recovery time

is proportional to the base transit time. Grove and

Sah[l I] have also pointed out that the switching process in a narrow base diode is entirely independent of carrier lifetime. P. Chaput and co-workers

[12] found that a minimum thickness of 2.5

diffusion lengths is needed to measure minority

carrier lifetime in 500 cm silicon with the photomagnetoelectric effect.

It can be generalized from this work and from

the works cited that diffusion length type measure- ments are inadequate characterization parameters

for bulk properties of semiconductor materials within a few diffusion lengths of a carrier source

or sink. However, when the effective diffusion length is in the transition range of djA to Id, the bulk diffusion length can be estimated from SPV

measurements. It is fortunate that under the conditions which yield an effective diffusion length rather than a bulk diffusion length measurement,

the effective value is often more useful.

It was also shown that the absorption characteristics of silicon are influenced by surface conditions

and that the SPV method provides a sensitive means

of observing differences in surface conditions.

Acknowledgements — Mc&suxQme^nt^ were made on

epitaxial silicon wafers supplied through the generosity

of Dr. F. L. Gittler and Bell Telephone Laboratories,

Allentown, Pennsylvania. Appreciation is expressed to Mr. A. W. Stallings for his ingenious fabrication of the equipment and for his care in making measurements and

to Mr. D. E. Sawyer for insights in the interpretation of both theory and experimental results. The contributions of Dr. W. M. Bullis to ail aspects to this work are also

gratefully acknowledged.

REFERENCES

1. A. M. Goodman, 7. appl. F/jyi. 32, 2550 { 1961).

2. F. Bergmann, C. Fritzsche and H. D. Riccius, Telefunken Ztg. 37, 186(1 964).

3. S. C. Choo and A. C. Sanderson, ^o/Zd-^r. Electron. 13,609(1970),

4. D. E. Sawyer and R. H. Rediker, Proc. Instn. Radio

Engrs. 46, 1 122 (1958).

5. N.J. Harrick,y. appl. Phys. 29. 764

6. N. H.Fletcher,J.£/ecrTO«. 2, 609(1957).

7. W. R. Runyan, Southern Methodist University

Report SMU 83-13 (1967). Also NASA CR 93154; and available from National Technical Information

Service as N68-I6510.

8. W. C. Dash and R. Newman, Phvs. Rev. 99, 1151

(1955).

9. E. Mendel and K. H. Yang, Proc. IEEE 57, 1476

(1969).

47
W. E. PHILLIPS

10. M. Byczkowski and J. R. Madigan,y. appl. Phys. 28, 878(1957).

11. A. S. Grove and C. T. Sah, Solid-St. Electron. 7, 107

(1964).

12. P. Chaput, D. Blanc, E. Casanovas, A. Peyre- Lavigne, A.-M. Chapuis and S. Soudain, Electronics

Lef/. 2, 223 (1966).

13. H. R. Philipp and E. A. Taft, Phys. Rev. 120, 37

(I960). APPENDIX

The experimental SPV data reported in this paper were

obtained by the following procedure. The epitaxial surface of the specimen was illuminated with a mechanically

chopped output of a monochromator at successive wavelengths of 0.80, 0.85, 0.90, 0.95, 0.97, 0.99, and 1 .00 ixm. The surface photovoltage signal was capacitively

coupled into a phase-sensitive lock-in amplifier syn- chronized with the mechanical chopper. The monochromator intensity was adjusted at each wavelength to produce a SPV signal of 250 /aV. A portion of the illumination was applied through an equivalent optical path to a thermopile detector whose output was detected

with a lock-in amplifier. To obtain a number proportional

to the photon intensity, !„. the output reading was

multiplied by the wavelength and by a term that corrects

for the slight wavelength dependence of the reflectivity

at the front surface of the specimen. This term (1 — /?)

is computed from a mathematical representation, valid for 0.7 < \ < 1.05 Aim, of the data of Philipp and Taft[i3];

1 - ^ = 0.6786 4- 0.03565A.-' -0.03149A.-2

These values of /o were plotted against the reciprocal

absorption coefficients for the corresponding wavelengths and a straight line was fitted to the points. A programmable desk calculator with a typewriter output was used

to process, plot, store and print out the data. A typical

print out is shown in Fig. 4. The specimen is the same as

in Fig. 1

.

The appropriate reciprocal absorption coefficients are calculated from a mathematical representation of the data

of Runyan[7] (for stress-relieved silicon) as: = [0.526367- 1.14425\-'-l-0.585368X-2 + 0.039958\-3]-'

or the data of Dash and Newman [8] (for lapped surfaces)

as:

a-' = [-1.06964 4-3. 34982X-'-3.61649A -2 + 1.3483U-^]-'.'

The calculation of the intercept, Lu, and the computed

one sigma standard deviation, si,„, is as follows:

WAVLLLIsGTH

1 . 000 vm

.\)90 .970

.950

. 900

.850

. 800

T t VOLTAGE

12 . 00 uV 10 . 00

7 .40 5.65

3 . <i5 2 . 35

1 . 80

fi m

RECIPR ABS COEFFI

1 34 . 306 pm 111.159

79.06 3 58.450

30. 797 18.032

1 1 . 269

INTENSITY

8.193

6.756

4.894

3.656

2 . 109

1. 352 .970

Lo= 4.9618^111 6IGHA

SPV SIGNAL = 250 uV

.4612 um SPECIMEN: EPI 3

Fig. 4. A programmable desk calculator plot and printout of a typical SPV measurement.

L„= {H„S^JS^,-la-')IN

N-2 \N^' )]'

where N is the number of data points,

5,,„ = 2V-(2/o)VN

5„ = 2 («-'/„) -2a-'S/o/N.

The tabulated intensity is !„ while the plotted intensity

is normalized to a maximum value of 5. All lengths are

in micrometers.

48
SUPPLEMENTARY BIBLIOGRAPHY: GOLD-DOPED SILICON

These entries are a supplement to those In an earlier bibliography [1],

They either were found or were published after the previous bibliography was

completed.

1962

Holonyak, N. , Jr., Double Injection Diodes and Related DI Phenomena in Semiconductors, Proc. IRE 50_, 2421-2428 (1962).

1965

Laurltzen, P. 0., Low-Frequency Generation Noise in Junction Field Effect

Transistors, Solid-State Eleotronias 8_, 41-58 (1965).

1966

Anantharaman , T. R. , Luo, H. L., and Klement, W. , Jr., Formation of New Intermetallic Phases in Binary Eutectic Systems by Drastic Undercooling of the

Melt, Nature 210, 1040-1041 (1966),

Aspnes, D. E., and Handler, P., Surface States on Cleaved (111) Silicon Surfaces, Surface Soi. 4_, 353-380 (1966).

Moore, J. S., Penchina, C. M. , Holonyak, N. , Jr., Sirkis, M. D., and Yamada,

T. , Electrical Oscillations in Silicon Compensated with Deep Levels, J. Appl.

Phys. 37, 2009-2013 (1966).

1967

Nassibian, A. G., Effect of Gold on Surface Properties and Leakage Current

of MOS Transistors, Solid-State Eleotronios 10, 891-896 (1967).

1968

Guttler, G., and Queisser, H. J., Impurity Photovoltaic Effect in Silicon,

VroQ, 7th Photovoltaic Specialists Conference^ Pasadena, California, 1968,

pp. 1-8 (IEEE, New York, 1968).

Lambert, J. L., and Reese, M. , The Gettering of Gold and Copper from Silicon,

Solid-state Electronics 11, 1055-1061 (1968).

Wu, S. Y., Theory of the Generation-Recombination Noise in MOS Transistors,

Solid-state Electronics 11, 25-32 (1968)

.

49
1969

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REFERENCE

1. Thurber, W. R. , and Bullis, W. M. , Resistivity and Carrier Lifetime in

Gold-Doped Silicon, Air Force Cambridge Research Laboratories Report

AFCRL-72-0076 (January 31, 1972). Available from National Technical

Information Service, Springfield, Virginia 22151, Accession Number

AD 740592.

53

FORM NBS-114A (1-71) U.S. DEPT. OF COMM. 1 . PU BLIC AT ION OR RE PORT NO. 2, Gov't Accession

BIBLIOGRAPHIC DATA

AFCRL-TR- 73-0107

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

RESISTIVITY AND CARRIER LIFETIME IN GOLD-DOPED SILICON.

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

W. Robert Thurber, David C. Lewis, and W. Murray Bullis

8. Performing Organization

9, PERFORMING ORGANIZATION NAME AND ADDRESS

\TINAIUJINAL A 'F Tr^\l AT tsUKtAU PlTIDfATT f~\ Urf blANUAKUo CT" A Tv7I^ A D rvc DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/ Work Unit No. 6096-04-01

11. Contract/Grant No. PRO Y-72~873

12. Sponsoring Organization Name and Address

AF Cambridge Research Laboratories (LQ) ' L. G. Hanscom Field

Bedford, Massachusetts 01730

13. Type of Report & Period

Covered Final

1 Tan - 31 Dpp 1Q7?

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES Performed as part of Joint Program on Methods of Measurement for

Semiconductor Materials, Process Control, and Devices with additional support from NBS

(cost center 4251126)

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This report describes the Current StatUS Of & con- tinuing study of the electrical properties of gold-doped silicon. Room Temperature re- sistivity and Hall effect measurements were made on many sets of gold-diffused boron- or phosphorus-doped silicon wafers for a wide range of initial resistivities of both types.

The general suitability of the proposed model was verified although an apparent discrepancy still remains between total and electrically active gold as confirmed by resistivity

data as a function of gold density for phosphorus-doped silicon. Electrical measurements

were made to study the activation energies of the gold donor and acceptor. In addition

the activation energy of the gold-coupled shallow acceptor in the proposed model was observed. The values found were in good agreement with other reported observations of

these levels. In the application of the surface photovoltage method to the measurement

of minority carrier lifetime, it was found that the optical absorption coefficients needed in the analysis of the data were dependent on the heat treatment given to the specimen. The uncertainty in diffusion length was determined to be about 2 ym which placed an effective lower limit on lifetime measurements of about 15 ns in p-type and about 50 ns

in n-type silicon. An analysis of the use of the surface photovoltage method for lifetime measurements in thin epitaxial layers is included as an appendix. The reverse re- covery (RR) technique for measuring lifetime was examined and it was observed that the

dependence of diode storage time on the ratio of forward to reverse current varied with

the base width of the diode studied. While theory and experiment for open circuit voltage decay (OCVD) were in agreement for long base width diodes, correlation for short base

diodes was less satisfactory; this study is continuing. Both the RR and OCVD techniques

give the same value of lifetime for long base diodes, but agreement for short base diodes

is not as good. Additional entries are included as a supplement to an earlier bibliography on the properties of gold-doped silicon.

17. KEY WORDS (Alphabetical order, separated by semicolons) Carrier lifetime; gold-doped siliCOn;

resistivity; semiconductor characterization: silicon.

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